Question

A block of mass $m$ is at rest relative to the stationary wedge of mass $M$. The coefficient of friction between block and wedge is $\mu$ . The wedge is now pulled horizontally with acceleration $a$ as shown in figure. Then the minimum magnitude of $a$ for the friction between block and wedge to be zero is:

• A. $\mu g\tan \theta$
• B. $g\cot \theta$
• C. $\mu g\cot \theta$
• D. $g\tan \theta$

Answer 1

The correct option is B $g\cot \theta$

Draw $FBD$ of block with respect to ground

The free body diagram of the block is as shown in the figure.
$N$ is the normal reaction exerted by wedge on the block.
The wedge moves towards left with acceleration $a$,
Then the component of acceleration of block normal to the plane is $a\sin \theta$

Find acceleration of wedge.
Applying Newton’s second law to the block normal to plane.
$mg\cos \theta -N=ma\sin \theta$
For $N$ to be zero
$mg\cos \theta =ma\sin \theta$
$a=g\cot \theta$

Final answer: Option(c)